Question

Calculate the requested measures for bonds A and B (assume each bond pays interest Semi-Annually:

Bond A: Coupon: 8%, YTM: 8%, Maturity (in years): 2, Par: 100.00, Price:100.000

Bond B: Coupon: 9%, YTM: 8%, Maturity (in years): 5, Par: 100.00, Price:104.055

A.) Calculate the duration for the two bonds by changing the yield up and down 25 basis points

B.) Calculate the duration for the two bonds by changing the yield up and down 10 basis points.

C.) Compare Your answers to parts (a) and (b).

Answer 1

	A	CALCULATION OF DURATION ;Changing yield up and down 25 basis point
		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=Semi annual YTM
		N=Semiannual Period of Cash Flow
		BOND A : Coupon 8%,Maturity 2 years
		Amount of semi annual coupon =(100*0.08)/2	$4
		Payment of principal at maturity	$100
		YTM up by 0.25%
		YTM =8+0.25=8.25%	0.0825
		Semi annualYTM=0.0825/2=	0.04125
		Number of semi annual periods of payment	4	(2*2)
		N	A	B=A/(1.04125^N)	C=N*A	D=C/(1.04125^N)
		Semi Annual Period	Cash flow	PV of cash flow	(Period)*(cash Flow)	PV of( Period* Cashflow)
		1	$4	3.841536615	$4	3.841536615
		2	$4	3.68935089	$8	7.378701781
		3	$4	3.543194132	$12	10.6295824
	(4+100)	4	$104	88.47351495	$416	353.8940598
			TOTAL	99.54759659		375.7438806
		Bond Duration in Semi annual period	3.77	(375.74/99.55)
		Bond Duration in years	1.89	Years
		BOND A : Coupon 8%,Maturity 2 years
		Amount of semi annual coupon =(100*0.08)/2	$4
		Payment of principal at maturity	$100
		YTM DOWN by 0.25%
		YTM =8-0.25=7.75%	0.0775
		Semi annualYTM=0.0775/2=	0.03875
		Number of semi annual periods of payment	4	(2*2)
		N	A	B=A/(1.03875^N)	C=N*A	D=C/(1.03875^N)
		Semi Annual Period	Cash flow	PV of cash flow	(Period)*(cash Flow)	PV of( Period* Cashflow)
		1	$4	3.85078219	$4	3.85078219
		2	$4	3.707130869	$8	7.414261738
		3	$4	3.568838382	$12	10.70651515
	(4+100)	4	$104	89.32832532	$416	357.3133013
			TOTAL	100.4550768		379.2848603
		Bond Duration in Semi annual period	3.78	(379.28/100.455)
		Bond Duration in years	1.89	Years
	B	CALCULATION OF DURATION ;Changing yield up and down 10 basis point
		BOND A : Coupon 8%,Maturity 2 years
		Amount of semi annual coupon =(100*0.08)/2	$4
		Payment of principal at maturity	$100
		YTM up by 0.1%
		YTM =8+0.1=8.1%	0.081
		Semi annualYTM=0.0825/2=	0.0405
		Number of semi annual periods of payment	4	(2*2)
		N	A	B=A/(1.0405^N)	C=N*A	D=C/(1.0405^N)
		Semi Annual Period	Cash flow	PV of cash flow	(Period)*(cash Flow)	PV of( Period* Cashflow)
		1	$4	3.844305622	$4	3.844305622
		2	$4	3.694671429	$8	7.389342859
		3	$4	3.550861537	$12	10.65258461
	(4+100)	4	$104	88.72888031	$416	354.9155213
			TOTAL	99.8187189		376.8017543
		Bond Duration in Semi annual period	3.77	(376.80/99.82)
		Bond Duration in years	1.89	Years
		BOND A : Coupon 8%,Maturity 2 years
		Amount of semi annual coupon =(100*0.08)/2	$4
		Payment of principal at maturity	$100
		YTM DOWN by 0.1%
		YTM =8-0.1=7.9%	0.079
		Semi annualYTM=0.0775/2=	0.0395
		Number of semi annual periods of payment	4	(2*2)
		N	A	B=A/(1.0395^N)	C=N*A	D=C/(1.0395^N)
		Semi Annual Period	Cash flow	PV of cash flow	(Period)*(cash Flow)	PV of( Period* Cashflow)
		1	$4	3.848003848	$4	3.848003848
		2	$4	3.701783404	$8	7.403566807
		3	$4	3.561119195	$12	10.68335759
	(4+100)	4	$104	89.07080238	$416	356.2832095
			TOTAL	100.1817088		378.2181378
		Bond Duration in Semi annual period	3.78	(378.22/100.18)
		Bond Duration in years	1.89	Years
	.(c)	THERE IS NO CHANGE IN BOND DURATION